For most Americans at the time secession wasn't legal or constitutional. For many who did believe secession constitutional it didn't justify the actions of the Confederacy that began the war. We could just as well talk of Davis and his co-conspirators as men who "chose to kill 5% of the US population" to get their own way.
"it didn't justify the actions of the Confederacy that began the war"
It was not actions of the Confederacy that began the war, but rather, inaction of the Union, specifically, Fort Sumter was sovreign Confederate territory, The C.S.A kindly asked the Union to remove their garrison from our territory. They refused, and after hearing that the fort was running out of supplies, they decided they were going to resupply the fort, and in doing so, they decided to violate sovreign Confederate maritime territory. The Republic of South Carolina, and more inclusively, the Confederate States of America, had every right to defend itself against what amounted to actions by a foreign power hostile to the nations existance.
The constitution was the contract. They broke that contract which is perfectly legal. The constitution doesn’t give the right to leave the Union because that is the contract, but the contract it self can be broken and that is what the south did.